Control Surveys and Coordinate Systems

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1 Control Surveys and Coordinate Systems The Earth is Round Basic Shape of the Earth: Oblate Spheroid of Revolution The length of the equatorial axis is approximately 27 miles greater than the polar axis. Average value of the Earth s radius: 20,906,000 ft GEODESY..

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3 Control Surveys and Coordinate Systems Horizontal Lattitude(φ): 0 is the Equator. Increases to 90 o N and 90 o S at the north and south poles. Longitude (λ): 0 is the Prime Meridian and runs through Greenwich England. These values increase to 180 o E and W. Vertical Mean Sea Level -Geodesists commonly call this surface the geoid -The geoidis a surface which is everywhere perpendicular to the plumb line (vertical or direction of gravity)

4 The Vertical Reference

5 The Horizontal Reference

6 The first Major adjustment in control Data was made in 1927 Resulting in the North American Datum of 1927; (NAD 27) The Reference Ellipsoid used was Clarke s Spheroid of 1866 Semimajor Axis: 6,378,206.4 m Semiminor Axis: 6,356,583.8 m The North American Datum of 1983 (NAD 83) The Reference Ellipsoid used was GRS80 Semimajor Axis 6,378,137.0 m Semiminor Axis 6,356,752.3 m Covers the North American Continent, Greenland, parts of Central America Geographic point in this system is latitude and longitude. Too cumbersome for everyday surveying (State Plane Grid), Used in Control Surveys (GPS) Angles, seconds MUSTbe carried out to at leastthe 4 th decimal place for Accuracies between NAD 83 1 st -order stations are better than 1:200,000-this is due to GPS.

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9 GRS80 Ellipsoid

10 NAD27, NAD83, WGS84 WGS84 NAD27 NAD83 Approximately 2 meters Earth Mass Center Approximately 236 meters GEOID WGS84 and NAD83 share the GRS80 ellipsoid but the origin differs by about 2m NAD27 uses the Clark spheroid of 1866, the origin is 236 m from WGS84

11 Principal Vertical Datums National Geodetic Vertical Datum of 1929 (NGVD 29) Superseded by NAVD 88 Normal Orthometric Heights North American Vertical Datum of 1988 (NAVD 88) Principal vertical datum for CONUS/Alaska Helmert Orthometric Heights

12 Geoid The equipotential surface of the Earth s gravity field which best fits, in the least squares sense, (global) mean sea level. * Geoid surface is neither visible or directly measureable. Geoid is mathematically related to and modeled from gravity data. A geoid height is the ellipsoidal height from an ellipsoidal datum to a geoid. Hence, geoid height models are directly tied to the geoid and ellipsoid that define them (i.e., geoid height models are not interchangeable). *Definition from the Geodetic Glossary, September 1986 Daniel R. Roman, National Geodetic Survey, National Oceanic and Atmospheric Administration

13 Geoid H = Orthometric Height (NAVD 88) h = Ellipsoidal Height (NAD 83) N = Geoid Height (GEOID 03) H = h - N h TOPOGRAPHIC SURFACE Ellipsoid (NAD 83) A Geoid (NAVD 88) H N Geoid Height (GEOID03) B

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15 Geoid DESIGNATION - LEV MAINT PID - DE9009 STATE/COUNTY- IL/CHAMPAIGN USGS QUAD - THOMASBORO (1975) *CURRENT SURVEY CONTROL * NAD 83(2007) (N) (W) ADJUSTED * NAVD (meters) 730. (feet) GPS OBS ELLIP HEIGHT (meters) (02/10/07) ADJUSTED GEOID HEIGHT (meters) GEOID03 SUPERSEDED SURVEY CONTROL ELLIP H (12/06/04) (m) ELLIP H (12/18/02) (m)

16 The GEOID03 Model The GEOID03 model is known as a hybrid geoid model, combining gravimetric information with GPS ellipsoid heights on leveled bench marks. The GEOID03 model was developed to support direct conversion between NAD 83 GPS ellipsoidal heights and NAVD 88 orthometric heights.

17 North American Datum Versions North American Datum of 1927 (NAD 27) Superseded by NAD 83 North American Datum of 1983 (NAD 83) Original release: NAD83(1986) 1997 adjustment: NAD83(1997) 2007 adjustment: NAD83(2007)

18 NAD 83 Evolution Summary 1986 original release Based on terrestrial data only 1997 adjustment Based on terrestrial and GPS data combined 2007 adjustment Based on GPS positions only Fixed to CORS network

19 Positional Accuracy Evolution TIME NETWORK LOCAL NETWORK SPAN ACCURACY ACCURACY NAD METERS (1 part in 100,000) NAD83(86) METER (1 part in 100,000) HARN METER B-order (1.0 ppm) A-order (0.1 ppm) CORS meter 0.01 meter

20 Positional Changes: KB0684 TIME POSITION DATUM SPAN Lat/Long/E Hgt POSITION SHIFT USSD/NAD Undetermined NAD m (13.73 ft) Undetermined NAD 83 (86) m (27.93 ft) Undetermined NAD 83 (97) m (1.45 ft) NAD 83 (07) (?) m (0.06 ft) m (0.03 ft) ITRF 2017?? (Predicted HTDP) 2017 (??) m (3.79 ft) m (4.06 ft)

21 High Accuracy Reference Network (HARN) A cooperative program started in 1986 by National Geodetic Survey (NGS) Started in TENNESSEE, and ended in Indiana in 1997

22 Control Network Redundancy!

23 TGRN

24 State Plane Coordinate Systems (SPCS) Two types: Lambert Conformal Conic Projection Transverse Mercator Projection Projecting a round surface onto a flat surface.

25 Transverse Mercator Projection

26 Lambert Conformal Conic Projection

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28 Tennessee State Plane Coordinate System N N False Easting Lambert Conformal Conic Projection

29 Lambert Conformal Conic Projection Intersection of cylinder cone and and ellipsoid SCALE EXACT Cone Ellipsoid

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31 State Plane Coordinates Grid Distances are Smaller than Geodetic Distances. Zones: the limits of a projection that do not exceed 158 miles (Lambert), so that the North-South distortions are 1/10,000 or less. Tennessee has only one zone.

32 We will address this again later

33 Kentucky State Plane Coordinate System 2 Zones to Minimize Distortion Lambert Conformal Conic Projection

34 Mississippi State Plane Coordinate System Transverse Mercator Projection 2 Zones to Minimize Distortion

35 Tennessee State Plane Coordinates Defined: TCA Title 66 Chapter 6 Units Designated by Law US Survey Feet

36 US Survey Foot vs International Foot 1 US Survey Foot = 12/39.37 meters = meters 1 meter = US Survey Feet 1 International Foot = exactly meters Some states use the International Foot in their State Plane grids. Illinois, Tennessee uses the US Survey Foot.

37 SPCS Distance Units Currently, NGS publishes SPCs for 7 states using the U.S. Survey Foot conversion factor 1 state using the International Foot conversion factor 42 states using only meters, not feet Based on STATE legislation we have or know about, 24 states have legislated the U.S. Survey Foot 8 states have legislated the International Foot 18 states have no legislation specifying conversion factor

38 North, What s the difference

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44 Lines of Lat and Lon and SPCS Grid Lines are Not the Same Distance: Scale Factor Scale = 1 at SCALE EXACT line Scale < 1 between SCALE EXACT lines Scale > 1 outside SCALE EXACT lines

45 Scale Factor Example 1 E1 = 10, ft on ellipsoid Scale = (average of scale at line endpoints) 10, ft X = ft Length of line G1 on grid

46 Scale Factor Example 2 20, ft X = 20, ft Length of line G2 on grid E2 = 20, ft on ellipsoid Scale = (average of scale at line endpoints)

47 Finding the Scale Factor

48 Finding the Scale Factor

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51 Grid to Ground Coordinates

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53 Effect of scaling coordinates Original SPCS Grid Coordinates Point ID Northing Easting SPCS Grid Coordinates scaled up to ground Scaled about origin by grid factor Grid coordinate grid factor = ground coordinate Point ID Northing Easting

54 Effect of scaling coordinates Distance too small to see the effect of scaling, although coordinates are scaled to be ground coordinates.

55 Effect of scaling coordinates Positional Shift in SPCS Grid Coordinates scaled up to ground Scaled about origin by grid factor Grid coordinate grid factor = ground coordinate Point ID Northing Easting Scaled coordinates are dangerous. They appear to be grid coordinates. So they MUST be DISCLOSED!!!

56 Ground Coord to Grid Coord D.A. Factor = 1/combined factor Combined Factor = scale factor * elevation factor Ground Coord/D.A. Factor = Grid Coord Grid N = / = Grid E = / =

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66 Common Test Questions: What are the origin coordinates for TN SPCS? Given a ground distance what would be the grid distance? Given a grid coordinate what is the ground coordinate?

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